关于拟正则隐式微分方程组的指数和阶
On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations
摘要：
本文主要研究拟正则隐式常微分代数方程（DAE）系统的微分指数和阶。给出了微分指数的代数定义，证明了阶与微分指数之和的Jacobi型上界。我们的技术也使我们能够获得另一种证明的Jacobi提出的组合界的顺序。作为我们的方法的结果，我们推导出一个上界的希尔伯特-Kolchin正则性和一个有效的理想的成员资格测试的拟正则隐式系统。最后，我们证明了隐式微分系统解的存在唯一性定理。
英文摘要：
This paper is mainly devoted to the study of the differentiation index and the order for quasi-regular implicit ordinary differential algebraic equation (DAE) systems. We give an algebraic definition of the differentiation index and prove a Jacobi-type upper bound for the sum of the order and the differentiation index. Our techniques also enable us to obtain an alternative proof of a combinatorial bound proposed by Jacobi for the order. As a consequence of our approach we deduce an upper bound for the Hilbert-Kolchin regularity and an effective ideal membership test for quasi-regular implicit systems. Finally, we prove a theorem of existence and uniqueness of solutions for implicit differential systems.
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